This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.
This work has been partially supported by grant # 6459/B/T02/2011/40 and by AGH.
Sawik, B. (2013), "Survey of multi-objective portfolio optimization by linear and mixed integer programming", Applications of Management Science (Applications of Management Science, Vol. 16), Emerald Group Publishing Limited, Bingley, pp. 55-79. https://doi.org/10.1108/S0276-8976(2013)0000016007
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